“A dead terrorist can’t cause any harm to Britain,” he said in December. “I do not believe that any terrorist, whether they come from this country or any other, should ever be allowed back into this country.”

Alexanda Kotey was one of two remaining members of a group of four British Isis fighters (BBC)

He and Mr Mattis spoke on Wednesday morning but officials have not announced the results of their discussions.

The US is coordinating information on captured foreign fighters with governments in the broad anti-Isis coalition, and American defence officials say they “generally expect these detainees to return to their country of origin for disposition”.

But Kotey and Elsheikh are believed to be among the dual nationals who joined Isis and have had their British citizenship removed for the “public good”.

Home Secretary Amber Rudd has refused to confirm they had been subjected to the Government measure, which aims to prevent militants returning to Britain.

“The important thing is that these two people face justice,” she said on Tuesday.

“We will always make sure that it’s properly coordinated and that they face justice.

“I can’t comment on individual cases, but we will always make sure that we keep everybody safe.”

The US has ruled out sending Kotey and Elsheikh to the Guantanamo Bay detention camp in Cuba, where terror suspects have been detained indefinitely without trial.

British hostage John Cantlie was shown in a series of Isis propaganda videos before disappearing during the battle of Mosul (AP)

Tobias Ellwood, a defence minister, has argued that the men should be tried at the International Criminal Court, but it can only act when countries are “unable or unwilling” to exercise their jurisdiction.

Kotey and Elsheikh were the last two members of the “The Beatles” to remain at large until they were detained by the SDF in eastern Syria last month.

They were wanted for involvement in the torture and execution of hostages, including the American journalist James Foley and British aid workers David Haines and Alan Henning, whose families have hailed the first step towards justice for their loved ones.

Intelligence extracted during interrogation by American officials has already sparked operations hunting down other jihadis, and could help searches for British hostage John Cantlie, security sources have told The Independent.

“The Beatles’” ringleader Jihadi John, whose real name was Mohammed Emwazi, was killed in a 2015 drone strike, and the fourth militant in the cell, Aine Davis, has been jailed for terror offences in Turkey.

Kotey and Elsheikh were declared “specially designated global terrorists” last year for their roles in the group, with officials holding the cell responsible for beheading more than 27 hostages and torturing many more.

A small number of captives, including French journalist Nicolas Henin, were freed and have told of the British militants’ brutality.

Mr Henin, who was released just four months before the group started beheading his former cellmates, said they should not be given the “satisfaction” of being put to death and becoming martyrs.

Mohammed Emwazi, known as Jihadi John, was pictured in an Isis propaganda magazine after being killed during a drone strike

“What I want is an incontestable trial,” he told The Independent. “I believe both former hostages and the families of those murdered largely share my feelings.

“We all are looking for justice. It will not bring us what we lost, a year in our life or even a son, but it’s still necessary.”

Relatives of Mr Haines and Mr Foley called for Kotey and Elsheikh to be locked up for the rest of their lives.

Elsheikh, 29, was said to have earned a reputation for waterboarding, mock executions and crucifixions while serving as a jailer, while fellow guard Kotey was involved in beheadings and known for “exceptionally cruel torture methods”, including electric shocks.

The 34-year-old is also accused of acting as an Isis recruiter and being responsible for drawing several other British extremists to join the terrorist group.

Born in London, Kotey is half-Ghanaian, half-Greek Cypriot and grew up in Shepherd’s Bush.

He is believed to have converted to Islam in his early twenties, and left two young children in Britain when he travelled to Gaza in 2009 as part of a controversial aid convoy organised by former Labour and Respect MP George Galloway.

Elsheikh came as a child from Sudan to the UK, where his family were granted refugee status, and became a mechanic in west London.

He had links to local gangs as a teenager, with his older brother jailed for gun possession, and was not known as religious until being introduced to a radical preacher.

Elsheikh travelled to Syria in 2012 and joined al-Qaeda’s regional branch before an internal dispute led to a splinter group creating Isis.

While Isis’s self-declared caliphate across Iraq and Syria has collapsed, leaving only small pockets of militants surrounded in border areas, it continues its efforts to inspire terror attacks around the world, and has expanded into countries including Afghanistan, Libya and Egypt.

Meanwhile, pioneering artificial intelligence technology that can prevent Isis propaganda videos from being uploaded was unveiled this week as the Government stepped up gathering evidence of online radicalisation.

Mr Williamson has vowed that Britain’s military would continue to attack Isis until its “poisonous global network” is destroyed.

The Royal Air Force has struck Isis targets 22 times in the past three weeks, the Defence Secretary told a coalition summit in Rome, adding: “We pledged to continue to fight terrorists until their poisonous global network is totally destroyed.

“Despite Daesh’s diminishing territory, it is hell-bent on directing and inspiring terrorist attacks worldwide – threatening our security at home and abroad.

“The threat they pose is evolving and intensifying, but our resolve to defeat them will not fade.”

Around 850 men, women and children travelled from the UK to Isis territories, including Syria and Iraq, with around half having returned and an unknown number being killed.